Problem: $f(x) = 4x^{2}+3$ What is the range of $f(x)$ ?
Consider the range of $4x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $4$ doesn't change the range. To get $4x^{2}+3$, we add $3$. So the range becomes: $\{\, y \mid y ≥ 3 \,\}$.